M4maths Previous Puzzles

18 Nov 2015 Share

Find the income derived from 44 shares of Rs.25 each at 5 premium (brokerage 1/4 per share), the rate of dividend being 5%. Mainly find the rate of interest on the investment.

OPtion

1) 3.25%
2) 4.55%
3) 4.85%
4) 5.25%
5) 4.95%
6) 5.65%
7) 3.75%
8) 5.45%
9) 4.15%
10)None of these

Solution

Cost of 1 share = Rs.(25 + 5 + 3/4)
= Rs. 171/4
Cost of 44 shares = Rs. (121/4 *44) = Rs. 1331
Therefore investment made = Rs. 1331
Now face value of 1 share = Rs. 25
Face value of 44 shares = Rs. 44*25 = Rs. 1100
Now, dividend on Rs. 100 = 11/2
Dividend on Rs. 1100 = Rs.(11/2*100 * 1100) = Rs. 60.50
Also income on investment of Rs. 1331 = Rs. 60.50
Income on investment of Rs. 100 = Rs. 60.50/1331 * 100
= 4.55 %
Option 2)

Correct Option: 2 Best Solution (4)

17 Nov 2015 Probability

A bag contain 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white

OPtion

1) 5/16
2) 1/26
3) 2/13
4) 1/5
5) 3/26
6) 1/16
7) 5/39
8) 1/39
9) 1/13
10)None of these

Solution

Let S be the sample space and E be the event of drawing 2 white balls.
Then, n(S) = Number of ways of drawing 2 balls out of 13
= 13 C 2 = 13*12/2 = 78
n(E) Number of ways of drawing 2 balls out of 5
5 C 2 = 5*4/2 = 10
Therefore
P(E) = n(E)/n(S) = 10/78 = 5/39
Option 7)

Correct Option: 7 Best Solution (23)

16 Nov 2015 Number

On dividing a number by 999, the quotient is 377 and the remainder is 105. The number is

OPtion

1) 476727
2) 364684
3) 476348
4) 376538
5) 376268
6) 359758
7) 376728
8) 434682
9) 359738
10)None of these

Solution

Number = (Divisor * Quotient) + Remainder
=999*377 + 105 = (1000-1)*377 + 105

= 376728

Option 7)

Correct Option: 7 Best Solution (6)

13 Nov 2015 Probability

A bag contain 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black.

OPtion

1) 3/5
2) 2/7
3) 1/3
4) 1/5
5) 1/4
6) 2/3
7) 2/5
8) 1/6
9) 1/7
10)None of these

Solution

n(s)=9C3
n(E)=(5C2*4C1)

p(E)=n(E)/n(S)
=(5C2*4C1)/9C3
=10/21

10/21

Option 10)

Correct Option: 10 Best Solution (6)

12 Nov 2015 Interest

A man lends Rs.10000 in four parts. If he gets 8% on Rs.2000, 7.5% on Rs.4000 and 8.5% part on Rs.1400, what percent must he get for the remainder, if the average interest is 8.13%

OPtion

1) 7%
2) 5%
3) 9%
4) 12%
5) 9.25%
6) 11.5%
7) 10.5%
8) 8%
9) 10.25%
10)None of these

Solution

Let required rate be x%
Then
2000*8*1/100 + 4000*15*1/2*100 + 1400*17*1/2*100 + 2600*x*1/100
= 10000*8.13*1/100
or 160+300+119+26x = 813
x = 9
Option 3)

Correct Option: 3 Best Solution (19)

11 Nov 2015 Banker's Discount

A bill for Rs.5656 is drawn on July, 14 at 5 months. It is discounted on October 5th at 5%. Find the money that the holder of the bill receives.

OPtion

1) 5589.65
2) 5568.88
3) 5556.56
4) 5686.86
5) 5678.67
6) 5599.44
7) 5579.47
8) 5689.66
9) 5688.44
10)None of these

Solution

Face value of the bill = Rs.5656
Date on which the bill was drawn = July, 14th at 5 months
Nominally due date = December, 14th
Legally due date = December, 17th
Date on which the bill was discounted October, 5th
Period for which the bill has yet to run
Oct, Nov, Dec.
26+30+17 days or 1/5 years

Note----------------
BD (Banker Discount) = SI on Rs.5656 for 1/5 years at 5%
= Rs.(5656*1*5 / 100*5) = Rs.56.56
TD(True Discount) = Rs.(5656*5*(1/5) / 100+(5*1/5) = Rs.56
BG(Banker Gain) = BD - TD = 56 Paise
-----------------

Money received by the holder of the bill
Rs.(5656-56.56) = Rs.5599.44
Option 6)

Correct Option: 6 Best Solution (6)

10 Nov 2015 Time and work

If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day, in how many days will 16 pumps raise 1736 tonnes, working 9 hours a day?

OPtion

1) 4 days
2) 5 days
3) 6 days
4) 7 days
5) 8 days
6) 9 days
7) 10 days
8) 12 days
9) 14 days
10)None of these

Solution

Less pumps, more days (Indirect)
Less water, less day (Direct)
More working hours, less day (Indirect)
Pumps 16:18
Water 2170:1736
Working hours 9:7

10:x
Solve x = 18*1736*7*10/16*2170*9 = 7 days
Option 4)

Correct Option: 4 Best Solution (28)

09 Nov 2015 Equation

Shweta and Sandhya solved a quadratic equation. In solving it, Shweta made a mistake in the constant term and got the roots as 6 and 2, while Sandhya made a mistake in the coefficient of x only and obtained the roots as -7 and -1. The correct root of the equation are.

OPtion

1) 6, -1
2) -7, 2
3) -6, -2
4) 7, 1
5) 7, -2
6) 7, 6
7) -7, -6
8) 3, 2
9) 6, 2
10)None of these

Solution

When there is no mistake in a and b, the sum of roots must be correct. When there is no mistake in a and c, product of the roots must be correct.
Therefore sum of roots = 6+2 = 8 and product of roots -7*-1 = 7
So the correct equation is x^2-8x+7
(x-7) (x-1)
The roots are 7, 1

Option 4)

Correct Option: 4 Best Solution (13)

06 Nov 2015 Volume

A cylindrical pencil of 2 cm diameter is sharpened so as to produce a perfect hemispherical portion at one end and a perfect conical portion of length 2 cm at the other end. Find the volume of shavings.

OPtion

1) 6.364 cm^3
2) 6.354 cm^3
3) 5.953 cm^3
4) 5.979 cm^3
5) 5.834 cm^3
6) 6.543 cm^3
7) 5.923 cm^3
8) 6.246 cm^3
9) 5.238 cm^3
10)None of these

Solution

For each portion
Volume of shavings = Volume of original cylindrical portion - Volume of final portion (Conical and Hemispherical)
and r = 1 cm
Volume of hemispherical portion = 2/3 Pi 1^3 = 2*Pi/3
Volume of conical portion = 1/3*Pi*1^2*2 = 2*Pi / 3
Total volume of cylindrical portion of both ends =
Pi(1)^2*1 + Pi(1)^2*2 = 3 Pi
Volume of shavings = Total volume of cylindrical portion - Volume of conical portion - Volume of hemispherical portion
3 Pi - 2Pi/2 - 2Pi/3 = 3Pi - 4Pi/3 = 5Pi/3
Using Pi = 22/7
5*22 / 21
5.238 cm^3
Option 9)

Correct Option: 9 Best Solution (2)

05 Nov 2015 Shares

A man wishes to invest Rs.2490. He invests Rs.900 in 7/2% stock at 75, Rs.850 in 3% at 68 and the remainder in 6% stock. If the total yield from his investment is 5%, at what price does he buy the 6% stock?

OPtion

1) 296/6
2) 267/2
3) 299/3
4) 89
5) 238/3
6) 237
7) 233/3
8) 112
9) 296/3
10)257/7

Solution

Income from 7/2% stock at 75 = Rs. 7/2*75 * 900 = Rs.42
Income from 3% stock at 68 = Rs. 3/68 * 850 = Rs. 37.50
Total income from these two stocks = Rs 79.50
But total income from the three stocks Rs. 5/100 * 2490 = Rs.124.50
Therefore Income from the third stock Rs. (124.50 - 79.50) = Rs.45
Investment in this case = Rs.2490 - (900+850) = Rs.740
If income is Rs.45, investment = Rs.740
If income is Rs.6, investment = Rs. 740/45 * 6 = 296/3
So he buys 6% stock at 296/3
Option 9)

Correct Option: 9 Best Solution (3)